What is the integral from 3 to x of sec(t)tan(t) ?

The integral from 3 to x of sec(t)tan(t) is sec(x)-sec(3)

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integral from 3 to x of sec(t)tan(t)

\int_{3}^{x} sec (t) tan (t) d t

sec (x) - sec (3)

Solution steps

\int_{3}^{x} sec (t) tan (t) d t

Apply u-substitution

: \int_{s e c (3)}^{s e c (x)} 1 d u

= \int_{s e c (3)}^{s e c (x)} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{s e c (3)}^{s e c (x)}

Simplify

= [u]_{s e c (3)}^{s e c (x)}

Compute the boundaries:

sec (x) - sec (3)

= sec (x) - sec (3)

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\int_{0}^{4} (x - 6)^{3} d x

What is the integral from 3 to x of sec(t)tan(t) ?
The integral from 3 to x of sec(t)tan(t) is sec(x)-sec(3)